Extended tumor-immunity surveillance modeldeterministic and stocastic analysis

In this thesis, the deterministic tumor cell-immune surveillance models that were previously defined were examined and the basic components of these models were identified one by one and a new tumor cell-immune surveillance model was created in accordance with the scientific literature. This model is based on the kinetic analysis method, which examines the development of tumor cells that escape from immune surveillance and tumor cells that fail to develop any escape mechanism (pure tumor cells) over time. Tumor cells that escape immune surveillance have been called wild tumor cells. A pure tumor cell immune surveillance model has been defined, primarily assuming that tumor cells do not escape immune surveillance. In order for this model to be biologically meaningful, the conditions in which model variables are positive and limited have been studied. The equilibrium points of the equation system, written in relation to the pure tumor cell model, were found and the basic reproduction number of the tumor-free balance point and the asymptotic stability and global stability States of the tumor-free balance point were examined. In the system of differential equations, the parameters defined as a result of immune interaction with tumor cell were redefined with random effect terms under normal distribution and generalized beta distribution, and the process of tumor cell immune interaction with the resulting random interaction model was studied. In addition, the results obtained for deterministic and random models were compared with the results of the model obtained as a result of stochastic effect and the interpretation of the model was provided. Finally, a wild tumor cell immune surveillance model was created by predicting tumor escape from immune cells, and the model was studied and interpreted under parameters modeled based on scientific assumptions.